Yes, it's a breeze. All the major cities have loads of hostels and many smaller touristy towns have at least one if not more. Have a look at Travellerspoint's list of Hostels in Australia to get an idea. You can either choose to just turn up and hope for a bed or book in advance if you prefer the certainty of a bed.

Yes, as peter says, it's really easy as there are hostels throughout Oz. Lonely Planet is a great guide to use if you are travelling independently and on a budget, and will list the hostels in each places. Most hostels will also be able to book tours, transport and activities, and if you stay in YHAs they can book rooms for you in other YHAs across Oz.

Lots of hostels have in-house travel agencys or tour desks that will book any activity/tour/transport you like. Travelling through Aussie is about as easy as you can get, and you'll find that most of the people you meet in hostels are solo travellers like yourself

Apart from the hostels that may have tour desks, having all the extra socialising with fellow travellers helps. Like you may be chatting to someone who has just come from some place or has been to a place on their trip that you didn't have on your list. What they say to you may sound good so you will go and travel there and also have a great time. When I have done my travelling overseas I have always found that a good thing and so far not been dissapointed when going to a place or staying at a place based on a fellow hosteller's opinion.

You will meet some very interesting characters and some great people at hostels, some of which you will probably keep in contact with and meet up to either travel with or visit at their home country on future trips. I've had this happen twice (and made many contacts that I remain in contact with).

As for the YHA hostels that bex76 mentions, unless you enjoy a less sociable/quieter scene and generally an older group of people, I would try and avoid staying at YHA hostels unless you have no other option. They are almost always the most expensive hostels in the city/town you are going to and also regularly they are not in a great location (away from the main things to see and so). They are the places where you stay if you want things picture perfect in the room, expensive internet, usually a locker and most the time included breakfast. It will be a rare YHA hostel that is a sociable one and will also be a rare one that is not squeeky clean. If you want a good nights sleep or want to stay in a dorm with the same sex rather than mixed, then they would be for you as this will almost always happen. Soemtimes this is a good situation, but most the time I found the other hostels more enjoyable (even as a person who is over the party 24/7 scene and prefers to go to bed early and wake up earlier).

Other people on the other hand (like bex, and like me) have had nothing but good experiences with YHAs in Australia, and will recommend them highly above the more run-down or party-oriented ("can't get a decent night's rest ever because of party-goers who keep entering at all hours of the night") alternatives.The very largest YHAs do sometimes feel like impersonal institutions, but any smaller hostels will be great, and I at least have never had trouble finding people to talk with in any YHA lounge. It's true YHAs are amongst the more expensive hostels, but the discount given by a YHA membership is also larger, so in the end that works out to exactly the same as any other hostel of the same quality. (There'll always be much cheaper very run-down places, but you really get what you pay for there.)

Just to provide some pushback... Which type of hostel you prefer really depends on what you personally are looking at.